Cox Regression interpretation with one factor variable?

Question

coxMod <- coxph(Surv(time, DEATH_EVENT) ~ anaemia, data=HF)
summary(coxMod)

Call:
coxph(formula = Surv(time, DEATH_EVENT) ~ anaemia, data = HF)

  n= 299, number of events= 96 

           coef exp(coef) se(coef)     z Pr(>|z|)  
anaemia1 0.3374    1.4013   0.2050 1.646   0.0998 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

         exp(coef) exp(-coef) lower .95 upper .95
anaemia1     1.401     0.7136    0.9376     2.094

Concordance= 0.545  (se = 0.027 )
Likelihood ratio test= 2.68  on 1 df,   p=0.1
Wald test            = 2.71  on 1 df,   p=0.1
Score (logrank) test = 2.73  on 1 df,   p=0.1

How would I read this? I understand having a factor and then adjusting for the continuous variable but what about one variable which is already a factor?

Would it be:

Anemic patients are 40% more likely to die than non-anemic patients

???

Is the fullmodel more valuable when it comes to interpretation due to adjusting how the model interacts with all other variables?

Call:
coxph(formula = Surv(time, DEATH_EVENT) ~ age + anaemia + creatinine_phosphokinase + 
    ejection_fraction + serum_creatinine + serum_sodium + hypertension, 
    data = HF)

  n= 299, number of events= 96 

                               coef  exp(coef)
age                       4.357e-02  1.045e+00
anaemia1                  4.460e-01  1.562e+00
creatinine_phosphokinase  2.101e-04  1.000e+00
ejection_fraction        -4.747e-02  9.536e-01
serum_creatinine          3.139e-01  1.369e+00
serum_sodium             -4.569e-02  9.553e-01
hypertensionPresent       4.965e-01  1.643e+00

Answer 1

Until you get to a point of overfitting, regression models are most reliable when you include as many outcome-associated predictor variables as reasonable, including properly specified associations of continuous predictors with outcome. That helps show effects of predictors that only become apparent when other predictors are accounted for, and can help avoid over-interpretation of an individually tested predictor whose association with outcome is primarily due to correlations with predictors that are more directly associated with outcome. The idea is to avoid omitted-variable bias.

Cox models are even more subject to omitted-variable bias than ordinary least squares regression. With a Cox model, you can have such bias even if an omitted predictor is uncorrelated with those in the model, similar to the situation with binomial regression.

Whether present as a single predictor or not, the coefficient for a two-level categorical predictor is the difference in log-hazard between its two levels when all other predictors are the same, and its exponentiation give the hazard ratio. With a multi-level categorical predictor and the default coding in R, you have a set of coefficients each representing a difference of a level from the reference level. I'm nevertheless hesitant to use your interpretation for the first model

Anemic patients are 40% more likely to die than non-anemic patients

because all patients are likely to die. It's a matter of how soon, or how likely at any given time point. I find it safest to stick with the technical term "hazard," which has a specific meaning in survival analysis.